scholarly journals Fractional Langevin equations with multi-point and non-local integral boundary conditions

2020 ◽  
Vol 7 (1) ◽  
pp. 1758361 ◽  
Author(s):  
Ahmed Salem ◽  
Mohammad Alnegga ◽  
Hari M. Srivastava
Keyword(s):  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
Langevin Equations ◽  
Integral Boundary ◽  
Local Integral ◽  
Non Local

scholarly journals Fractional Langevin Equations with Nonlocal Integral Boundary Conditions

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 402 ◽  
Author(s):  
Ahmed Salem ◽  
Faris Alzahrani ◽  
Lamya Almaghamsi
Keyword(s):  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
Langevin Equations ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Nonlinear Alternative ◽  
Banach Contraction ◽  
Nonlocal Integral Boundary Conditions ◽  
Fractional Orders

In this paper, we investigate a class of nonlinear Langevin equations involving two fractional orders with nonlocal integral and three-point boundary conditions. Using the Banach contraction principle, Krasnoselskii’s and the nonlinear alternative Leray Schauder theorems, the existence and uniqueness results of solutions are proven. The paper was appended examples which illustrate the applicability of the results.

scholarly journals Existence of Solution for a Fractional Langevin System with Nonseparated Integral Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Lahcen Ibnelazyz ◽  
Karim Guida ◽  
Khalid Hilal ◽  
Said Melliani
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Existence Of Solution ◽  
Langevin Equations ◽  
Integral Boundary ◽  
Type Integral

In this paper, we investigate the existence and uniqueness of a coupled system of nonlinear fractional Langevin equations with nonseparated type integral boundary conditions. We use Banach’s and Krasnoselskii’s fixed point theorems to obtain the results. Lastly, we give two examples to show the effectiveness of the main results.

scholarly journals Addendum: Salem, A. et al. Fractional Langevin Equations with Nonlocal Integral Boundary Conditions. Mathematics 2019, 7, 402

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1030
Author(s):  
Salem ◽  
Alzahrani ◽  
Almaghamsi
Keyword(s):  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
Langevin Equations ◽  
Integral Boundary ◽  
Nonlocal Integral Boundary Conditions

The authors wish to make the following corrections to this paper [...]

scholarly journals Coupled System of Nonlinear Fractional Langevin Equations with Multipoint and Nonlocal Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Ahmed Salem ◽  
Faris Alzahrani ◽  
Mohammad Alnegga
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Research Paper ◽  
Langevin Equations ◽  
Integral Boundary ◽  
Nonlocal Integral Boundary Conditions

This research paper is about the existence and uniqueness of the coupled system of nonlinear fractional Langevin equations with multipoint and nonlocal integral boundary conditions. The Caputo fractional derivative is used to formulate the fractional differential equations, and the fractional integrals mentioned in the boundary conditions are due to Atangana–Baleanu and Katugampola. The existence of solution has been proven by two main fixed-point theorems: O’Regan’s fixed-point theorem and Krasnoselskii’s fixed-point theorem. By applying Banach’s fixed-point theorem, we proved the uniqueness result for the concerned problem. This research paper highlights the examples related with theorems that have already been proven.

scholarly journals Fractional Langevin Equations with Nonseparated Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Khalid Hilal ◽  
Lahcen Ibnelazyz ◽  
Karim Guida ◽  
Said Melliani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Integral Boundary Conditions ◽  
Langevin Equations ◽  
Banach Fixed Point Theorem ◽  
Integral Boundary ◽  
Main Work ◽  
Krasnoselskii Fixed Point Theorem

In this paper, we discuss the existence of solutions for nonlinear fractional Langevin equations with nonseparated type integral boundary conditions. The Banach fixed point theorem and Krasnoselskii fixed point theorem are applied to establish the results. Some examples are provided for the illustration of the main work.

scholarly journals Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 174
Author(s):  
Chanakarn Kiataramkul ◽  
Weera Yukunthorn ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Integral Boundary ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Banach Contraction Mapping Principle

In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the existence and uniqueness of solutions of the considered system, by using standard fixed point theorems, such as Banach contraction mapping principle and Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.

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